We report on a measurement of the polarization in the decay
$B^0 \rightarrow J/\psi K^{\ast 0}$ using data collected at the Collider
Detector at Fermilab in $\overline{p} p$ collisions at $\sqrt{s} = 1.8$ TeV.
$B^0$ mesons were reconstructed through the decay chain
$B^0 \rightarrow J/\psi K^{\ast 0}, J/\psi\rightarrow \mu^+ \mu^-,
K^{\ast 0} \rightarrow K^+ \pi^-$. The result, based on a sample of $60\pm 11$
events, is $\Gamma_L/\Gamma = 0.66 \pm 0.10$ (stat) $+0.08\atop-0.10$ (sys).